Q: A sample of sodium-24 ($$^{24}\mathrm{Na}) $$has a decay constant $$k = 4.63 \times 10$$^{-2}$$\ \mathrm{h}^{-1}. $$What is its half-life ($$t_{1/2}$$)? Use $$t_{1/2} = \frac{0.693}{k}.$$

$$t_{1/2} = \frac{0.693}{4.63 \times 10$$^{-2}$$} = 15.0\ \mathrm{h}$$

Q: If you start with 100 g of sodium-24, how much remains after 30 hours? ($$k = 4.63 \times 10$$^{-2}$$\ \mathrm{h}^{-1}) $$Use $$N = N_0$ e$$^{-kt}$$.

$$N = 100 e$$^{-4.63 \times 10^{-2}$$ \times 30} = 24.0\ \mathrm{g}$$

Q: A scientist finds an ancient scroll and measures its carbon-14 content to be 25% of that in living plants. If the half-life of carbon-14 is 5730 years, estimate the age of the scroll.

$$2 \times 5730 = 11,460$$ years

Question 1

Which of the following statements best distinguishes a nuclear reaction from a chemical reaction?

Accepted Answer

A nuclear reaction changes the atomic nucleus, often resulting in a different element, while a chemical reaction involves only the rearrangement of electrons.

Question 2

Which of the following nuclear equations is correctly balanced?

Accepted Answer

$$^{238}_{92}\mathrm{U} \$$rightarrow ^{4}$$_{2}\mathrm{He} $$+ ^{234}$$_{90}\mathrm{Th}$$

Question 3

What is the change in atomic number and mass number when an atom undergoes beta ($$\beta^-) $$emission?

Accepted Answer

Atomic number increases by 1; mass number remains unchanged.

Question 4

Which radioactive decay process results in the emission of a particle with 2 protons and 2 neutrons?

Accepted Answer

Alpha emission

Question 5

A sample of sodium-24 ($$^{24}\mathrm{Na}) $$has a decay constant $$k = 4.63 	imes 10$$^{-2}$$\ \mathrm{h}^{-1}. $$What is its half-life ($$t_{1/2}$$)? Use $$t_{1/2} = \frac{0.693}{k}.$$

Accepted Answer

$$t_{1/2} = \frac{0.693}{4.63 	imes 10$$^{-2}$$} = 15.0\ \mathrm{h}$$

Question 6

If you start with 100 g of sodium-24, how much remains after 30 hours? ($$k = 4.63 	imes 10$$^{-2}$$\ \mathrm{h}^{-1}) $$Use $$N = N_0$ e$$^{-kt}$$.

Accepted Answer

$$N = 100 e$$^{-4.63 	imes 10^{-2}$$ 	imes 30} = 24.0\ \mathrm{g}$$

Question 7

Which of the following best describes why carbon-14 dating is effective for determining the age of ancient organic materials?

Accepted Answer

Living organisms maintain a constant ratio of carbon-14 to carbon-12, but after death, carbon-14 decays and is not replaced.

Question 8

Which process is represented by the following nuclear equation: $$^{131}_{53}\mathrm{I} \$$rightarrow ^{131}$$_{54}\mathrm{Xe} $$+ ^{0}$$_{-1}\mathrm{e}$$?

Accepted Answer

Beta emission

Question 9

Which of the following is true about the energy changes in nuclear versus chemical reactions?

Accepted Answer

Nuclear reactions release much more energy than chemical reactions.

Question 10

A radioactive isotope decays with a half-life of 10 hours. What fraction of the original sample remains after 30 hours?

Accepted Answer

$$\left(\frac{1}{2}\$$right)^3$$ = \frac{1}{8}$$

Question 11

Which of the following changes occurs during positron emission?

Accepted Answer

Atomic number decreases by 1; mass number remains unchanged.

Question 12

Which type of radioactive decay does NOT change the atomic number or mass number of the nucleus?

Accepted Answer

Gamma emission

Question 13

A scientist finds an ancient scroll and measures its carbon-14 content to be 25% of that in living plants. If the half-life of carbon-14 is 5730 years, estimate the age of the scroll.

Accepted Answer

$$2 	imes 5730 = 11,460$$ years

Question 14

Which of the following is a correct statement about isotopes in nuclear reactions?

Accepted Answer

Different isotopes of the same element can behave very differently in nuclear reactions.

Question 15

Which of the following is a first-order process?

Accepted Answer

Radioactive decay

Question 16

Which of the following best explains why balancing nuclear equations is important?

Accepted Answer

The number of nucleons and the charge must be conserved in a nuclear reaction.

Nuclear Chemistry: Radioactivity, Nuclear Reactions, and Radioactive Decay

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